N.Y. Jud. Law § 474
The compensation of an attorney or counsellor for his services is governed by agreement, express or implied, which is not restrained by law, except that no agreement made hereafter between an attorney and a guardian of an infant for the compensation of such attorney, dependent upon the success of the prosecution by said attorney of a claim belonging to said infant, or by which such attorney is to receive a percentage of any recovery or award in behalf of such infant or a sum equal to a percentage of any such recovery or award, shall be valid or enforceable unless made as hereinafter provided. An attorney may contract with the guardian of an infant to prosecute, by suit or otherwise, any claim for the benefit of an infant for a compensation to said attorney dependent upon the success in the prosecution of such claim, subject to the power of the court, as hereinafter provided, to fix the amount of such compensation. Whenever such a contract shall have been entered into between an attorney and a guardian of an infant, upon the recovery of a judgment, or the obtaining of an award in behalf of the said infant, or upon any compromise or settlement of such claim, the attorney may apply, upon notice to the guardian, to the judge, justice or surrogate before whom the said action or proceeding was tried, or to whom an application for compromise or settlement was made, in case the said action or proceeding was tried, or the said application was made at a court held within this state; or to a special term of said court, in case the said action or proceeding was tried before some person other than a justice thereof, or said claim was compromised or settled after said suit was begun, or in case of the death or disability of the judge or justice before whom the action was tried; or to special term of the supreme court in case the recovery, award, compromise or settlement was not had in any court of this state. Such application shall set forth briefly the contract, the services performed by the attorney and pray that there be awarded to him a suitable amount out of the recovery, award, compromise or settlement obtained through his efforts as attorney on behalf of the infant. The court, judge or surrogate to which such application is made, upon being satisfied that due notice of the said application as been given to the said guardian, shall proceed summarily to determine the value of the services of said attorney, taking such proof from either the attorney or the guardian by affidavit, reference or the examination of witnesses before the said court, judge or surrogate, as may seem to be necessary and proper, and shall thereupon make an order determining the suitable compensation for the attorney for his services therein, which sum shall thereafter be received by the said attorney for his services in behalf of the said infant; and no other compensation shall be paid or allowed by the guardian for such services out of the estate of said infant. If a copy of such order awarding the compensation with notice of entry be thereafter served by the said attorney upon the adverse party to the said litigation or the person making such compromise or settlement and upon the custodian of the funds recovered, in case there be such custodian, such award shall become and constitute a lien to the amount thereof on behalf of the said attorney upon such recovery, award, settlement or fund.
N.Y. Jud. Law § 474